Dynamics random walks on Heisenberg groups

Nadine Guillotin-Plantard (1) , René Schott (2, 3)

1 ICJ - Institut Camille Jordan
2 IECN - Institut Élie Cartan de Nancy
3 LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications

We prove a Guivarc'h law of large numbers and a central limit theorem for dynamic random walks on Heisenberg groups. The limiting distribution is explicitely given. To our knowledge this is the first study of dynamic random walks on non-commutative Lie groups.

Mots clés: dynamic random walks; group theory; dynamical systems; Lévy stochastic area

Domaines: Probabilités [math.PR]

Nadine Guillotin-Plantard, René Schott. Dynamics random walks on Heisenberg groups. Journal of Theoretical Probability, 2006, 19, pp.377-395. ⟨hal-00135062⟩